Question

give the center and radius of the circle described by the equation and graph the equation. use the graph to identify the domain and range.
$(x + 2)^{2}+(y + 6)^{2}=25$
the center is
(type an ordered pair. simplify your answer.)

Explanation:

Step1: Recall the standard form of a circle's equation

The standard form of a circle's equation is \((x - h)^{2}+(y - k)^{2}=r^{2}\), where \((h,k)\) is the center and \(r\) is the radius.

Step2: Rewrite the given equation in the standard form

Given \((x + 2)^{2}+(y + 6)^{2}=25\), we can rewrite it as \((x-(- 2))^{2}+(y-(-6))^{2}=5^{2}\).

Answer:

\((-2,-6)\)